Mean estimation through proportion estimation

In this work a device which changes the problem of mean estimation into that of proportion estimation is proposed. The device consists of perturbing the observations. The goal of the work is the construction of conservative confidence intervals for means. Three applications are given: (1) proportion estimation in the context of cluster random sampling, (2) differences of proportions of a multinomial population and (3) variance estimation.     

Lystematic sampling of two-dimensional surfaces and related problems

The paper is largely concerned with twenty-one possible methods of sampling a plane area, with points as sampling units, for the purpose of estimating a portion of this area having certain defined characteristics. These methods result from a combination, two at a time, of random, stratified and systematic sampling in two perpendicular directions, with or without alignment of the sampled points. Eleven of these methods involve systematic sampling in one or both directions. The estimate of the proportion of the area of interest is simply the proportion of points in the total area, falling within the area having the defined characteristics. For each method the variance function is derived. Fourteen different types of space covariance functions are involved in these variance functions.     

Optimal Variable Sample Size and Sampling Interval MSE Chart Based on Improved Square Root Transformation

In the field of statistical process control (SPC), control charts for attributes are widely used to detect the out-of-control condition by checking the number of nondefective units or nondefective in a sample. In this article, we use the average time to signal (ATS) and the average number of observations to signal (ANOS) to evaluate the performance of the optimal variable sample size and sampling interval (VSSI) improved square root transformation (ISRT) mean square error (MSE) (VSSI_ ISRT_ MSE) control chart for attribute data. In addition, this control chart will be used to monitor: (1) the difference between the process mean and the target value, and (2) the process variance shifts. We found that the optimal VSSI_ ISRT_ MSE chart performs better than the specific VSSI, the optimal variable sampling interval (VSI), and the fixed parameters (FP) ISRT_MSE charts. An example is given to illustrate this new proposed approach.     

Two-Stage Cluster Sampling with Ranked Set Sampling in the Secondary Sampling Frame

Motivated by a real-life problem, we develop a Two-Stage Cluster Sampling with Ranked Set Sampling (TSCRSS) design in the second stage for which we derive an unbiased estimator of population mean and its variance. An unbiased estimator of the variance of mean estimator is also derived. It is proved that the TSCRSS is more efficient—in the sense of having smaller variance—than the conventional two-stage cluster simple random sampling in which the second-stage sampling is with replacement. Using a simulation study on a real-life population, we show that the TSCRSS is more efficient than the conventional two-stage cluster sampling when simple random sampling without replacement is used in both stages.     

Improving The Efficiency of The Case-Crossover Design

The case-crossover design has been used by many researchers to study the transient effect of an exposure on the risk of a rare outcome. In a case-crossover design, only cases are sampled and each case will act as his/her own control. The time of failure acts as the case and non failure times act as the controls. Case-crossover designs have frequently been used to study the effect of environmental exposures on rare diseases or mortality. Time trends and seasonal confounding may be present in environmental studies and thus need to be controlled for by the sampling design. Several sampling methods are available for this purpose. In time-stratified sampling, disjoint strata of equal size are formed and the control times within the case stratum are used for comparison. The random semi-symmetric sampling design randomly selects a control time for comparison from two possible control times. The fixed semi-symmetric sampling design is a modified version of the random semi-symmetric sampling design that removes the random selection. Simulations show that the fixed semi-symmetric sampling design improves the variance of the random semi-symmetric sampling estimator by at least 35% for the exposures we studied. We derive expressions for the asymptotic variance of risk estimators for these designs, and show, that while the designs are not theoretically equivalent, in many realistic situations, the random semi-symmetric sampling design has similar efficiency to a time-stratified sampling design of size two and the fixed semi-symmetric sampling design has similar efficiency to a time-stratified sampling design of size three.     

Estimation of a rare sensitive attribute in a stratified two-stage unrelated randomized response model by using Poisson probability distribution

The present article deals with the estimation of mean number of respondents who possess a rare sensitive character in presence of known and unknown proportion of a rare unrelated non-sensitive attribute by using the Poisson probability distribution in stratified random sampling as well as in stratified random double sampling. The variance of rare sensitive character is also derived under proportional and optimal allocation methods in stratified random sampling when stratum sizes are known and unknown. The properties of the suggested estimation procedures have been deeply examined. The proposed model is found to be dominant over Lee et al. [Estimation of a rare sensitive attribute in a stratified sample using Poisson distribution. Statistics. 2013;47:575–589] model. Numerical illustrations are presented to support the theoretical results. Results are analysed and suitable recommendations are put forward to the survey practitioners.     

Finite Population Variance Estimation Under LSS with Multiple Random Starts

In this article, an unbiased estimator for finite population variance is developed under linear systematic sampling with two random starts and an explicit expression for its variance is also obtained. The study is supported by two real life situations. A detailed numerical comparative study has been carried out to compare its average variance with the average variance of the conventional unbiased estimator for finite population variance under simple random sampling for a wide variety of populations. Results based on the study strongly favor the use of the developed estimator for such populations.     

Cluster designs to assess the prevalence of acute malnutrition by lot quality assurance sampling: a validation study by computer simulation

Summary.  Traditional lot quality assurance sampling (LQAS) methods require simple random sampling to guarantee valid results. However, cluster sampling has been proposed to reduce the number of random starting points. This study uses simulations to examine the classification error of two such designs, a 67×3 (67 clusters of three observations) and a 33×6 (33 clusters of six observations) sampling scheme to assess the prevalence of global acute malnutrition (GAM). Further, we explore the use of a 67×3 sequential sampling scheme for LQAS classification of GAM prevalence. Results indicate that, for independent clusters with moderate intracluster correlation for the GAM outcome, the three sampling designs maintain approximate validity for LQAS analysis. Sequential sampling can substantially reduce the average sample size that is required for data collection. The presence of intercluster correlation can impact dramatically the classification error that is associated with LQAS analysis.     

An efficient non-rejective implementation of the πps sampling designs

Poisson sampling is a method for unequal probabilities sampling with random sample size. There exist several implementations of the Poisson sampling design, with fixed sample size, which almost all are rejective methods, that is, the sample is not always accepted. Thus, the existing methods can be time-consuming or even infeasible in some situations. In this paper, a fast and non-rejective method, which is efficient even for large populations, is proposed and studied. The method is a new design for selecting a sample of fixed size with unequal inclusion probabilities. For the population of large size, the proposed design is very close to the strict πps sampling which is similar to the conditional Poisson (CP) sampling design, but the implementation of the design is much more efficient than the CP sampling. And the inclusion probabilities can be calculated recursively.     

Design effect of randomized systematic sampling

In statistical practice, systematic sampling (SYS) is used in many modifications due to its simple handling. In addition, SYS may provide efficiency gains if it is well adjusted to the structure of the population under study. However, if SYS is based on an inappropriate picture of the population a high decrease of efficiency, i.e. a high increase in variance may result by changing from simple random sampling to SYS. In the context of two-stage designs SYS so far seems often in use for subsampling within the primary units. As an alternative to this practice, we propose to randomize the order of the primary units, then to select systematically a number of primary units and, thereafter, to draw secondary units by simple random sampling without replacement within the primary units selected. This procedure is more efficient than simple random sampling with replacement from the whole population of all secondary units, i.e. the variance of an adequate estimator for a total is never increased by changing from simple random sampling to randomized SYS whatever be the values associated by a characteristic with the secondary units, while there are values for which the variance decreases for the change mentioned. This result should hold generally, even if our proof, so far, is not complete for general sample sizes.     

Variance Estimation under Two‐Phase Sampling

We consider the variance estimation of the weighted likelihood estimator (WLE) under two‐phase stratified sampling without replacement. Asymptotic variance of the WLE in many semiparametric models contains unknown functions or does not have a closed form. The standard method of the inverse probability weighted (IPW) sample variances of an estimated influence function is then not available in these models. To address this issue, we develop the variance estimation procedure for the WLE in a general semiparametric model. The phase I variance is estimated by taking a numerical derivative of the IPW log likelihood. The phase II variance is estimated based on the bootstrap for a stratified sample in a finite population. Despite a theoretical difficulty of dependent observations due to sampling without replacement, we establish the (bootstrap) consistency of our estimators. Finite sample properties of our method are illustrated in a simulation study.     

Robust sampling strategies for regression estimation

For probability linear regression estimation, conditions are derived where sampling will be robust against violations of the commonly assumed heterogeneous variance model. Stratified pps (spps) and stratified random sampling (spscx) are shown to satisfy these conditions approximately and are more efficient generally than restricted simple random sampling (RSRS) for some real populations and for artificial populations with weights of k = 0, 0.5, 1.0, 1.5 and 2.0. The criteria needs some additional refinement to better predict relative efficiency of spps and spscx.     

Estimation of the Change Point in Monitoring the Process Mean and Variance

Knowing the time of a process change could lead to quicker identification of the special cause and less process down time, as well as help to reduce the probability of incorrectly identifying the special cause. In this article, we propose the maximum likelihood estimator (MLE) for the process change point when a control chart with the fixed sampling rate (FSR) scheme or the variable sampling rate (VSR) scheme is used in monitoring a process to detect changes in the process mean and/or variance of a normal quality variable. We investigate the performance of this estimator when it is used in various types of control charts.     

Large sample behavior of entropy measures when parameters are estimated

In this paper, we study the asymptotic behavior of (h,π)-entropy statistics when the parameters are replaced by some consistent and asymptotically normal (CAN) estimates. In the case of stratified sampling, asymptotic distribution is obtained and the optimum allocation is derived for a fixed cost and for a fixed variance. Some tests of hypotheses are constructed on the basis of these asymptotic distributions and a numerical example is presented.     

Sample-based Maximum Likelihood Estimation of the Autologistic Model

New recursive algorithms for fast computation of the normalizing constant for the autologistic model on the lattice make feasible a sample-based maximum likelihood estimation (MLE) of the autologistic parameters. We demonstrate by sampling from 12 simulated 420×420 binary lattices with square lattice plots of size 4×4, …, 7×7 and sample sizes between 20 and 600. Sample-based results are compared with ‘benchmark’ MCMC estimates derived from all binary observations on a lattice. Sample-based estimates are, on average, biased systematically by 3%–7%, a bias that can be reduced by more than half by a set of calibrating equations. MLE estimates of sampling variances are large and usually conservative. The variance of the parameter of spatial association is about 2–10 times higher than the variance of the parameter of abundance. Sample distributions of estimates were mostly non-normal. We conclude that sample-based MLE estimation of the autologistic parameters with an appropriate sample size and post-estimation calibration will furnish fully acceptable estimates. Equations for predicting the expected sampling variance are given.     

Fitting Variance Components Model and Fixed Effects Model for One-Way Analysis of Variance to Complex Survey Data

Under complex survey sampling, in particular when selection probabilities depend on the response variable (informative sampling), the sample and population distributions are different, possibly resulting in selection bias. This article is concerned with this problem by fitting two statistical models, namely: the variance components model (a two-stage model) and the fixed effects model (a single-stage model) for one-way analysis of variance, under complex survey design, for example, two-stage sampling, stratification, and unequal probability of selection, etc. Classical theory underlying the use of the two-stage model involves simple random sampling for each of the two stages. In such cases the model in the sample, after sample selection, is the same as model for the population; before sample selection. When the selection probabilities are related to the values of the response variable, standard estimates of the population model parameters may be severely biased, leading possibly to false inference. The idea behind the approach is to extract the model holding for the sample data as a function of the model in the population and of the first order inclusion probabilities. And then fit the sample model, using analysis of variance, maximum likelihood, and pseudo maximum likelihood methods of estimation. The main feature of the proposed techniques is related to their behavior in terms of the informativeness parameter. We also show that the use of the population model that ignores the informative sampling design, yields biased model fitting.     

Median Estimation Using Double Sampling

This paper proposes a general class of estimators for estimating the median in double sampling. The position estimator, stratification estimator and regression type estimator attain the minimum variance of the general class of estimators. The optimum values of the first-phase and second-phase sample sizes are also obtained for the fixed cost and the fixed variance cases. An empirical study examines the performance of the double sampling strategies for median estimation. Finally, an extension of the methods of Chen & Qin (1993) and Kuk & Mak (1994) is considered for the double sampling strategy.     

Estimation of finite population mean in simple and stratified random sampling using two auxiliary variables

We propose an improved difference-cum-exponential ratio type estimator for estimating the finite population mean in simple and stratified random sampling using two auxiliary variables. We obtain properties of the estimators up to first order of approximation. The proposed class of estimators is found to be more efficient than the usual sample mean estimator, ratio estimator, exponential ratio type estimator, usual two difference type estimators, Rao (1991) estimator, Gupta and Shabbir (2008) estimator, and Grover and Kaur (2011) estimator. We use six real data sets in simple random sampling and two in stratified sampling for numerical comparisons.     

Some calibration estimators for finite population mean in two-stage stratified random sampling

Abstract

In the present article, an effort has been made to develop calibration estimators of the population mean under two-stage stratified random sampling design when auxiliary information is available at primary stage unit (psu) level. The properties of the developed estimators are derived in-terms of design based approximate variance and approximate consistent design based estimator of the variance. Some simulation studies have been conducted to investigate the relative performance of calibration estimator over the usual estimator of the population mean without using auxiliary information in two-stage stratified random sampling. Proposed calibration estimators have outperformed the usual estimator without using auxiliary information.     

Accelerated life test sampling plans for the Weibull distribution under Type I progressive interval censoring with random removals

This paper considers the design of accelerated life test (ALT) sampling plans under Type I progressive interval censoring with random removals. We assume that the lifetime of products follows a Weibull distribution. Two levels of constant stress higher than the use condition are used. The sample size and the acceptability constant that satisfy given levels of producer's risk and consumer's risk are found. In particular, the optimal stress level and the allocation proportion are obtained by minimizing the generalized asymptotic variance of the maximum likelihood estimators of the model parameters. Furthermore, for validation purposes, a Monte Carlo simulation is conducted to assess the true probability of acceptance for the derived sampling plans.